Adding and subtracting rational numbers worksheet with answers – Embark on an in-depth exploration of rational number operations with our comprehensive worksheet, complete with detailed answers. This guide delves into the fundamental concepts of rational numbers, empowering you to confidently perform addition and subtraction operations.

Through a structured approach, we will guide you through the intricacies of adding and subtracting rational numbers, regardless of their signs. Our meticulously crafted examples and step-by-step instructions ensure a thorough understanding of the underlying principles.

Adding and Subtracting Rational Numbers

Rational numbers are numbers that can be expressed as a fraction of two integers, where the denominator is not zero. They include both positive and negative numbers, and they can be represented on a number line. Rational numbers are used in many real-world applications, such as measuring distances, calculating speeds, and determining probabilities.

Adding Rational Numbers

To add two rational numbers with the same sign, simply add their numerators and keep the denominator the same. For example, 1/2 + 1/2 = 2/2 = 1.

To add two rational numbers with different signs, first find a common denominator. Then, add the numerators and keep the common denominator. For example, 1/2 + (-1/3) = 3/6 + (-2/6) = 1/6.

Subtracting Rational Numbers

To subtract two rational numbers with the same sign, simply subtract the smaller numerator from the larger numerator and keep the denominator the same. For example, 1/2 – 1/4 = 2/4 – 1/4 = 1/4.

To subtract two rational numbers with different signs, first find a common denominator. Then, subtract the smaller numerator from the larger numerator and keep the common denominator. For example, 1/2 – (-1/3) = 3/6 – (-2/6) = 5/6.

Worksheet and Answers

Worksheet:

1. Add: 1/2 + 1/4
2. Add:
   

   1/3 + 1/6

3. Subtract: 1/2
   

   1/4

4. Subtract:
   • 1/3
   • 1/6

Answers:

1. 3/4
2. 1/6
3. 1/4
4. -1/2

Practice and Applications, Adding and subtracting rational numbers worksheet with answers

Here are some additional practice problems:

1. Add:
   

   1/2 + 1/3

2. Subtract: 1/4
   

   (-1/6)

Rational number operations are used in a variety of real-world applications, such as:

• Measuring distances
• Calculating speeds
• Determining probabilities

Answers to Common Questions: Adding And Subtracting Rational Numbers Worksheet With Answers

What are rational numbers?

Rational numbers are numbers that can be expressed as a fraction of two integers, where the denominator is not zero.

How do I add rational numbers with the same sign?

To add rational numbers with the same sign, simply add their numerators and keep the same denominator.

How do I subtract rational numbers with different signs?

To subtract rational numbers with different signs, subtract the numerator of the smaller fraction from the numerator of the larger fraction and keep the same denominator. If the result is negative, place a negative sign in front of the fraction.